please explain
6. (3 points) What is the largest integer p such that f(n) = 10 log n+100 log(n3)+2(log n)2 is ⌦((log n)p)? A. p = 2 B. p = 3 C. p = 4 D. p = 5 E. p = 6
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6. (3 points) What is the largest integer p such that f(n) = 10...
6. What is the asymptotic solution to the recurrence relation T(n) = 3T(n/2)+n3 log(n)? please explain
6. What is the asymptotic solution to the recurrence relation T(n) = 3T(n/2)+n3 log(n)? please explain
Please solve Q1, this is a discrete math question. "O" represents Oh notation, f=O(g) if there...
Please solve Q1, this is a discrete math
question. "O" represents Oh notation, f=O(g) if there are positive
constants c and n0 such that for any n≥ n0,
f(n) ≤ c·g(n). Please include all your explanations.
Problem 1 (3 points) Find the least integer t such that (n° + n2 log(n)) (log(n) + 1) + (8 log(n) +6) (n3 + 4) is 0 (nt). Briefly justify your answer (i.e., why it is o (nt) and why it is not 0...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
For each pair of functions determine if f(n) ? ?(g(n)) or f(n) ? ?(g(n)) or f(n)...
For each pair of functions determine if f(n) ? ?(g(n)) or f(n) ? ?(g(n)) or f(n) ? O(g(n)) and provide a proof as specified. For each of the following, give a proof using the definitions. 1. f(n) = log(n), g(n) = log(n + 1) 2. f(n) = n3 + nlog(n) ? n, g(n) = n4 + n 3. f(n) = log(n!), g(n) = nlog(n) 4. f(n) = log3(n), g(n) = log2(n) 5. f(n) = log(n), g(n) = log(log(n))
if possible solve part d in detail. a) fi(n) n2+ 45 n log n b) f:(n)-1o+...
if possible solve part d in detail.
a) fi(n) n2+ 45 n log n b) f:(n)-1o+ n3 +856 c) f3(n) 16 vn log n 2. Use the functions in part 1 a) Isfi(n) in O(f(n)), Ω(fg(n)), or Θ((6(n))? b) Isfi(n) in O(f(n)), Ω(f,(n)), or Θ((fs(n))? c) Ísf3(n) in O(f(n)), Ω(f(n)), or Θ(f(n))? d) Under what condition, if any, would the "less efficient" algorithm execute more quickly than the "more efficient" algorithm in question c? Explain Give explanations for your answers...
b. 6 e. 32 a. 2 c. 10 d. 14 31. Place the following ions in...
b. 6 e. 32 a. 2 c. 10 d. 14 31. Place the following ions in order of increasing radius: Ali, F, Mg2., and N3. a. F< Mg2+ < N3- < Al 3+ b. F <N3- <A13+ < Mg2+ c. F< N3- < Mg2+ < Al 3+ d. N3- <F. < Mg2+ < Al 3+ e. Al 3+ < Mg2+ < F< N3- 32. Place the following atoms in order of increasing ionization energy C, N, and Si a. C<N<...
9. (5 points) Please describe an algorithm that takes as input a list of n integers...
9. (5 points) Please describe an algorithm that takes as input a list of n integers and finds the number of negative integers in the list. 10. (5 points) Please devise an algorithm that finds all modes. (Recall that a list of integers is nondecreasing if each term of the list is at least as large as the preceding term.) 11. (5 points) Please find the least integer n such that f() is 0(3") for each of these functions f()...
) 6. Let x be the binomial random variable with n = 10 and p =...
) 6. Let x be the binomial random variable with n = 10 and p = .9 (2) a. Find P(x = 8) (5) b. Create a cumulative probability table for the distribution. (2) c. Find P( x is less than or equal to 7) (2) d. Find P(x is greater than 7) e. Find the mean, μ. (1) f. Find the standard deviation, σ. (1) g. Find the variance. ...
6. (10 points) A 2D data x is given below. Find the 3-stage integer wavelet transform...
6. (10 points) A 2D data x is given below. Find the 3-stage integer wavelet transform (IWT) for x. Use (1,1) integer wavelet transform. (a) Find the matrix xl after column transform in the first stage. 8x8 (b) Find the matrix X2 after row transform in the first stage. 8x8 (c) Find the matrix x3 after column transform in the second stage. 4x4 (d) Find the matrix x4 after row transform in the second stage. 4x4 (e) Find the matrix...
Problem (2), 10 points Let n be an integer. Prove that if 3 does not divide n, then 3(2n2 5)
Problem (2), 10 points Let n be an integer. Prove that if 3 does not divide n, then 3(2n2 5)
Problem (2), 10 points Let n be an integer. Prove that if 3 does not divide n, then 3(2n2 5)
Please solve Q1, this is a discrete math
question. "O" represents Oh notation, f=O(g) if there are positive
constants c and n0 such that for any n≥ n0,
f(n) ≤ c·g(n). Please include all your explanations.
Problem 1 (3 points) Find the least integer t such that (n° + n2 log(n)) (log(n) + 1) + (8 log(n) +6) (n3 + 4) is 0 (nt). Briefly justify your answer (i.e., why it is o (nt) and why it is not 0...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
if possible solve part d in detail.
a) fi(n) n2+ 45 n log n b) f:(n)-1o+ n3 +856 c) f3(n) 16 vn log n 2. Use the functions in part 1 a) Isfi(n) in O(f(n)), Ω(fg(n)), or Θ((6(n))? b) Isfi(n) in O(f(n)), Ω(f,(n)), or Θ((fs(n))? c) Ísf3(n) in O(f(n)), Ω(f(n)), or Θ(f(n))? d) Under what condition, if any, would the "less efficient" algorithm execute more quickly than the "more efficient" algorithm in question c? Explain Give explanations for your answers...
b. 6 e. 32 a. 2 c. 10 d. 14 31. Place the following ions in order of increasing radius: Ali, F, Mg2., and N3. a. F< Mg2+ < N3- < Al 3+ b. F <N3- <A13+ < Mg2+ c. F< N3- < Mg2+ < Al 3+ d. N3- <F. < Mg2+ < Al 3+ e. Al 3+ < Mg2+ < F< N3- 32. Place the following atoms in order of increasing ionization energy C, N, and Si a. C<N<...
9. (5 points) Please describe an algorithm that takes as input a list of n integers and finds the number of negative integers in the list. 10. (5 points) Please devise an algorithm that finds all modes. (Recall that a list of integers is nondecreasing if each term of the list is at least as large as the preceding term.) 11. (5 points) Please find the least integer n such that f() is 0(3") for each of these functions f()...
6. (10 points) A 2D data x is given below. Find the 3-stage integer wavelet transform (IWT) for x. Use (1,1) integer wavelet transform. (a) Find the matrix xl after column transform in the first stage. 8x8 (b) Find the matrix X2 after row transform in the first stage. 8x8 (c) Find the matrix x3 after column transform in the second stage. 4x4 (d) Find the matrix x4 after row transform in the second stage. 4x4 (e) Find the matrix...
Problem (2), 10 points Let n be an integer. Prove that if 3 does not divide n, then 3(2n2 5)
Problem (2), 10 points Let n be an integer. Prove that if 3 does not divide n, then 3(2n2 5)
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